Revealing mistake: When the coconut flies at Peter, there are a couple of flashes of light reflected from the device used to connect wire to the coconut.
Revealing mistake: As Peter pulls himself up to look over the brick wall, the entire snow drift on top moves, showing it's set dressing.
Revealing mistake: As Tink flies around waking up the Lost Boys, as she flies by the red-headed kid, the wires operating the puppet are visible.
Answer: Neverland very much runs on "If you believe, it will happen" which is what Tink means during the meal when she says "If you don't imagine yourself as Peter Pan you won't be Peter Pan." So by the rules of Neverland, as soon as Peter believed it was real it was then real. The dinner was trying to teach him to believe as, in Neverland, if you don't believe it then it won't happen.